ABSTRACT This study presents a comprehensive numerical investigation of buoyancy‐driven boundary‐layer flow and heat transfer of viscoelastic (non‐Newtonian) fluids over a horizontal surface subjected to two fundamental thermal boundary conditions: constant surface temperature (CST) and constant heat flux (CHF). Using similarity transformations, the governing nonlinear partial differential equations are reduced to a coupled system of ordinary differential equations and solved to examine the influence of the Prandtl number (0.7 ≤ Pr ≤ 100) and the viscoelastic parameter (0.10 ≤ A ≤ 0.21) on velocity and temperature fields, boundary‐layer thickness, wall shear stress, and the modified Nusselt number. The results show that increasing viscoelasticity suppresses buoyancy‐driven convection, leading to reduced peak velocities, thicker momentum and thermal boundary layers, lower wall shear stress, and reduced heat transfer rates under both CST and CHF conditions. Increasing the Prandtl number from 0.7 to 100 enhances near‐wall temperature gradients, significantly thins the thermal boundary layer, and increases the Nusselt number, with a stronger influence observed under CST conditions. A key finding is that CHF exhibits significantly greater sensitivity to viscoelastic effects than CST due to the dynamic adjustment of wall temperature required to sustain a prescribed heat flux, which amplifies elastic damping and modifies buoyancy forces. The study highlights the coupled roles of fluid elasticity and thermal diffusion and demonstrates that neglecting viscoelastic effects can lead to overestimation of heat transfer performance. The results provide design‐oriented insights for thermal energy storage, electronic cooling, polymer processing, and other applications involving buoyancy‐driven transport of viscoelastic fluids.
Maaitah et al. (Sat,) studied this question.